Aún no tenemos significados para "choose arbitrarily".
1Thus (G) may be chosen arbitrarily, and also parts of (P); all these laws are conventions.
2These book-marks cannot be chosen arbitrarily.
3These sections have been chosen arbitrarily, i.e., {1}, {2}
4The point A was chosen arbitrarily, but it is evident that that of the needles depends on its distance from the point of convergence.